iOS icloud email account sent messages show my name not recipients

I have several issues with emails in my Sent mailboxes in the iCloud account on my iPhone (iOS 9.3.1). First: mails sent from my MacBook Air and iMac are synced to the iCloud email account on my iPhone in the Sent folder that actually has a folder icon. Instead of the recipient's name, however, all I see is my own. If I click on the mail, it opens up and I can see the recipient, but I want it to show the recipient in the list of Sent mails. If I send a mail from the iPhone itself, the mail appears in the other Sent folder (the one with a piece of folded paper that looks like a jet) but with family name first. I don't want to be anal about this, but I would love to know how I can get all my Sent mail, regardless of which device it is sent from, to appear in one Sent folder (preferably the jet-like one) showing recipients' names with given name first, family name second. That's what happens with my other two mail accounts. Any help appreciated.